Evaluation of CO2 Injectivity From Waterflood Values

SPE 132624Evaluation of CO 2 Injectivity from Waterflood ValuesVenu Nagineni, SPE, and Richard G. Hughes, SPE, Louisiana State University; David D'Souza, SPE, and Kenneth M. Deets, SPE, Denbury Resources Inc.Copyright 2010, Society of Petroleum EngineersThis paper was prepared for presentation at the SPE Western Regional Meeting held in Anaheim, California, USA, 27–29 May 2010.This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.AbstractCarbon dioxide flooding is a common IOR method employed in fields which have relatively easy access to CO 2. In some cases, estimating the CO 2 injection rate is the most important design parameter which decides the planning, field implementation and eventual success of a flood. This paper presents a method for evaluating this important parameter from data that should be readily available for a field.Water injectivity index values from fields which have undergone waterflood operations are compared to injectivity index values for the same field while undergoing CO 2 flood operations. Different methods for evaluating the indices are presented as is a process for estimating the CO 2 injectivity value from data from secondary operations.The correlation developed has been verified on injectors which were converted in the same field. Initial injection rates calculated from this correlation were in closer agreement to actual injection rates than those predicted by other theoretical formulas.BackgroundDuring the planning of a waterflood or enhanced oil recovery operation, an engineer has to estimate injection rates at a specified injection pressure in order to size equipment and evaluate flood performance and economics. Often these estimates are obtained from simulation studies or from analytic or semi-analytic solutions published for the flood pattern being proposed.A broad method to estimate injection rates for CO 2 injection wells is using relative rate ratios. A ratio of an average of the CO 2 injection rates to an average of the water injection rates is calculated for each well in a field and an average of these ratios is used to calculate the CO 2 injection rate for a new well using the available water injection data from that well.Theoretical relationships to calculate injection rate for different flood patterns have been presented by Muskat (1949). These mathematical models were derived considering steady-state flow in a homogenous formation. As an extension of these analytical models, Prats, et al (1959) presented a method to predict water injection rate for a reservoir having wide range of permeability values. However, these relationships are applicable only for a flood with unit mobility ratio. Most gas floods have a mobility ratio much greater than one, so these relations do not work well for gas injection. Caudle and Witte (1959) used experimental models to develop a correlation between injection rate, mobility ratio and areal sweep efficiency. They studied the variation of conductance with mobility ratio and flood front advance. These models are very well applied and verified for waterflood systems.For a five-spot flood, Muskat (1949) presented analytical solutions for injectivity in unit mobility ratio floods as2688.0log 001538.0,−∆=winj water r dPh q λ(1)Deppe (1961) presented a semi-analytical solution for essentially the same problem but which can be applied for systems with non-unit mobility ratio. For the five-spot pattern, the injectivity is given by()wpep wi ei wp wi u inj water r r r rP P h q loglog 003076.0,+−=λ(2)2 SPE 132624When the producer and injector radii are equal, the Deppe (1961) injectivity equation differs from the Muskat (1949) equation by a small change in the constant term in the denominator. One notable advantage of Deppe’s model is the flexibility of being able to use different well radii for injection and production wells. In addition, λu (the mobility of the reservoir fluid) allows the application of this relationship to fluid systems with different mobility ratios. Deppe (1961) also showed the application of his methodology to other flood patterns with similar results.Rearranging Eqn. 2 in the form of an injectivity index yields()wpep wi ei uwp wiinjwater r r r rh P Pq loglog 003076.0,+=−λ (3)For a given reservoir, pattern and fluid system, the right hand side of Eqn. 3 should be approximately constant afterbreakthrough. Hence, plotting the left hand side (injectivity index) over time should result in an approximately constant value. However, P wi and P wp are not always measured during field operations; hence the denominator can be altered in terms of an average reservoir pressure which can either be measured or estimated. The injectivity index would then be().,res wiinjwater P Pq y Index Injectivit −=(4)All these relationships are for a waterflood using reservoir volumes or assume water is incompressible. In order to apply these relationships to a gas flood system some modifications need to be made to account for the properties exhibited by gases, mainly the lower viscosity and higher compressibility values. One way to account for these factors, similar to productivity evaluation, would be to assume the product of the gas viscosity and z-factor terms are approximately constant yielding the traditional P 2 technique (Lee and Wattenbarger, 1996). Thus injectivity index, computed through()2res2fbhpconditionsreservoir gas,gas ..P Pq I I −=(5)plotted against time should be approximately constant. Lee and Wattenbarger (1996) showed that the P 2 technique is viable at fairly low pressures. A better approach would be to use the pseudo-pressure technique (Al-Hussainy, et al., 1966). This would yield())()(..res fbhpconditionsreservoir gas,gas P m Pm q I I −=(6)where the m(P) terms are the real gas pseudo-pressures defined by (Al-Hussainy, et al., 1966)()∫=PP bdp Z p P m µ2(7)A simple ratio of the waterflood flow rate to the gas injection flow rate would neglect both the viscosity differences betweenthe water and the gas and the density changes that occur through the P 2 or m(P) contributions and should not be expected to yield reasonable results. The P 2 formulation takes into account some of the compressibility changes that occur with gas systems, but does so accurately only at low pressures. Thus we would expect that the appropriate form of the injectivity index should be Eqn. 6.MethodologyTo confirm our assumption that the pseudo-pressure calculated injectivity index would yield more accurate estimates of the injectivity values for CO 2 systems, the following steps were used in this work:1. Field data of surface injection pressure, volume injected and estimated average reservoir pressures were obtained forwells which were initially water injectors and were later converted to CO 2 injection.2. Water and CO 2 injectivity indices (using Equations 4, 5 and 6) were calculated and plotted versus time to observeany trend. In order to calculate CO 2 injectivity index, the surface injection pressure for the well was converted to a bottomhole pressure using a Microsoft Excel ® macro.3. Trends of water and CO 2 injectivity indices from this process were cross plotted to obtain a correlation.All the equations to calculate injectivity index need an input of flowing bottomhole pressure (FBHP). For a water injection well, FBHP can be calculated by the addition of the hydrostatic head to the wellhead pressure, and subtracting any frictional losses. However for gases density varies with temperature and pressure. Hence, density needs to be accounted for in all ensuing equations to calculate FBHP.SPE 132624 3 Lee and Wattenbarger (1996) describe the average temperature and z-factor method used to calculate the FBHP. This method uses an iterative calculation to obtain pressure at the end of selected depth intervals. A Microsoft Excel® macro was built to estimate FBHP by dividing the entire well depth into a number of smaller depth intervals. Pressure changes were then calculated for each interval, beginning from the top. Density and z-factor of CO2 in each interval were estimated using the average temperature and pressure in the interval. The summation of pressure changes over all such depth intervals and subtracting frictional losses gives the FBHP. Values of FBHP calculated using the macro were compared to measured FBHP data available for some of the wells. A small error ranging between -0.25% and 2% was observed between the two as shown in Table 1.Injection data were collected from two oil fields in Mississippi. Field-1 had data from 5 wells that were water injection wells which were later converted to CO2 injectors. Of these five wells, data from four wells are discussed at length in this paper. The fifth well was excluded because it had similar injectivity index trends as one of the other four wells. Field-2 had data from 8 wells that were converted from water injection to CO2 injection. Injectivity indices from six of the wells from Field-2 were used to build a correlation while the other two wells were used to verify the correlation. Wells from each field have been designated as Well-1a, Well-1b and so on for wells from Field-1, and similarly Well-2a, Well-2b and so on for wells from Field-2. Figures 1 through 8 show well and field plots of water and CO2 injectivity indices for the two selected fields. Only monthly injection data were available so injectivity indices are plotted on a common time axis in order to make trend comparison easier.Field-1For Field-1, CO2 injection pressure data were not available for the initial several years of injection. Therefore data for CO2 injectivity index in Figures 1 through 6 starts from the first month of the availabile pressure data. For instance Well-1b had no injection pressure data available for the first 7 years of injection, while Well-1d had no injection pressure data available for nearly 13 years.Figure 1 is a plot of all injectivity indices for Well-1a. Water injectivity indices (WII) lie approximately on a straight line parallel to the x-axis and hence can be assumed to be an approximately constant value. Similar observation can be made for CO2 injectivity indices (CII) calculated using the pseudo-pressure technique whereas CO2 injectivity indices calculated using the P2technique are much more scattered and do not really follow any trend. Well-1b (Figure 2) has similar characteristics, but with much less scatter in the CO2injectivity indices calculated using the P2technique which have an approximately constant value. This is the only case where an almost constant value was found using the P2 technique. Well-1c (Figure 3) and Well-1d (Figure 4) again show scattered data for the P2 technique with much less scatter for both the water injectivity indices and the CO2 injectivity indices using the pseudo-pressure technique. The water injectivity plots for Well-1d shown in Figure 4 have a greater variation in the values for WII than the other wells and could be approximated as either a decreasing trend or multiple constant values that varied in time. As with the other wells in the field, a mean value for the water injectivity was calculated.The figures described above show that water injectivity indices are approximately uniform during the period the field was under waterflood. However, CO2injectivity indices calculated using different equations show different trends. CO2 injectivity index values were almost uniform with time when calculated using the pseudo-pressure relationship whereas CO2 injectivity index calculated using the P2 relationship were more scattered. Based on these observations it was concluded that obtaining a correlation between water and CO2 injectivity indices would be more useful if the pseudo-pressure relationship (Eqn. 6) was used for CO2 injectivity index.These same graphs for the wells in Field-1 were re-plotted without the P2 technique values. Wells 1a, 1b and 1c were plotted separately from Well-1d to highlight some differences between their WII. Well-1d has greater variation of WII, ranging between 0 - 7 bbl/day/psi (Figure 6), whereas the other three wells combined have WII ranging between 0 - 2.5 bbl/day/psi (Figure 5). Table 2 lists the mean and standard deviation values for the Water and pseudo-pressure CO2 injectivity indices for all wells in Field-1.An average of these injectivity indices for each well can be calculated, cross-plotted, and used for a correlation. However, as this particular field has no recent CO2 conversions with which we could verify the correlation’s usefulness. We use the data from this field primarily to explain the observed uniform trends in injectivity indices and also to suggest that these indices could be correlated. Another field, Field-2, was selected precisely for the purpose of generating a correlation and verifying it.Field-2Plots similar to the ones described above were constructed using injection data from wells in Field-2. Data from six different injection wells were used in constructing these plots. Unlike Field-1, CO2injection data for the wells in Field-2 were available from the beginning of the CO2 flood. Including water and CO2 injectivity indices of all six wells in one plot would make it hard to observe trends of the data points; hence the plots are separated into two groups, each with injectivity indices of three wells. Figures 7 and 8 show the injectivity indices of Wells-2a, 2d, 2f, and Wells-2b, 2c, 2e, respectively. Well 2c (Figure 8) and Well 2d (Figure 7) have a large scatter to the water injectivity data and both show a drastic drop in the final few months of injection. The remaining wells have a much smaller spread. For several of the wells, it is unclear as to whether an approximately constant value should be used to represent the data or some trend. Wells 2a and 2f appear to have a similar constant value (Figure 7) but Well 2a has an almost step change in WII during the last 20 months of injection. Wells 2b and4 SPE 1326242e have what appear to be inclined trends for much of their data, but both drop to values that are approximately at the mean during their last several months of injection.Field-2 has significantly less CO 2 injection data available when compared to Field-1. Due to the small number of data points, long-term trends cannot be clearly identified in any of the CO 2 injectivity index data. An average value of these CII was calculated to represent each well’s CO 2 injectivity index. Though this may not be a good representation for CII as the flood progresses, this approximation should be reasonable for the evaluation of the initial CO 2 injectivity for wells being converted from water injection. Table 2 lists the mean and standard deviation for Water and CO 2 injectivity indices for the wells in Field-2.Correlation and VerificationThe average reservoir pressure for Field-2 was estimated from the measured well bottomhole pressure data if it was available or a value of 2400 psia as an estimate of the field average reservoir pressure if it was not. This pressure was used in all ensuing calculations for WII and CII. The averages of water and CO 2 injectivity indices for all six wells from Field-2 were cross plotted in order to build a correlation. The correlation coefficient (R 2) for a linear trend line from these data was low. In an attempt to increase the R 2 value, the average reservoir pressure for each well was iteratively modified. We assumed that errors in the estimated values of the average reservoir pressure around each well were ±10% of the original 2400 psia value. The resulting adjusted average reservoir pressure values for each well lie between 2250 and 2550 psia (±6.25% of the initial estimate of average reservoir pressure).Figure 9 shows the final cross plot and the resulting linear trend line through the data. The linear trend equation relates water and CO 2 injectivity indices for Field-2 and is given by56109983.5105044.3−−×+×=WII CII(8)The value of the correlation coefficient (0.646), although not as high as we would like it to be, suggests that a correlation exists between injectivity indices and that a linear trend captures nearly 65% of the variability in the releationship. A correlation coefficient of 0.646 can be interpreted as a moderate relationship between the variables. For Field-2, in the future, if any water injectors are converted into CO 2 injectors, one can use this correlation to calculate a CO 2 injectivity index from the average of the water injectivity indices for the well and thereby estimate the initial CO 2 injection rate.The next step in the process was to verify this correlation on one or more of the wells which were recently converted into CO 2 injectors. Two wells in Field-2 were converted to CO 2 injectors and each had six months of injection data. The correlation was then used to estimate the initial injection rate (the average injection rate for the first 5 days) for these two wells. The two wells that were chosen to verify the correlation will be referred as ‘Verification Well #1’ and ‘Verification Well #2’. In order to verify the correlation, water injectivity indices for these two wells were plotted (Figure 10) and an average of these values was calculated. By substituting this average water injectivity index into the correlation equation obtained above (Eqn. 8), the estimated CO 2 injectivity index values for the two wells were calculated.Calculating Injection Rate from Injectivity IndexOnce the estimated value for CO 2 injectivity index for both the Verification Wells were computed, the equation for CO 2 injectivity index (Equation 6) now has two known values and two unknown values. The known values are CO 2 injectivity index and average reservoir pressure whereas, the unknown values are CO 2 injection rate and flowing bottomhole pressure. If the wellbore parameters for a well are known both these unknown values can be related by the well tubing performance relationship (TPR). Figures 11 and 12 show the tubing performance curves for Verification Well #1 and Verification Well #2, respectively. These were plotted by assuming a constant wellhead pressure and using the wellbore data available for these wells. The wellhead pressures used were the recorded wellhead pressures for the two wells, averaged over the first five days.Selecting any point on this TPR curve and by substituting its corresponding flowing bottomhole pressure into the injectivity equation will result in a theoretical flow rate. Repeating this step a number of times for different points on the TPR curve would give several theoretical injection rates. The locus of these theoretical injection rates intersects the TPR curve at a single point. This intersection point is the estimated injection rate for each Verification Well. In case of Verification Well #1, the initial injection rate obtained from the graph (Figure 11) was 2.74 MMSCFD whereas the actual average injection rate was 2.19 MMSCFD (a 25% relative error). For Verification Well #2, the initial injection rate obtained from the calculation procedure was 4.87 MMSCFD and the actual average injection rate was 4.97 MMSCFD (a 2% relatve error). These two estimated values are reasonably close to the measured initial injection values especially considering that the estimated rates obtained by the relative ratio method gives 8 MMSCFD and 12 MMSCFD for the two wells.ConclusionsBased on this work, the following conclusions can be made:1. CO 2 injectivity index values calculated through the pseudo-pressure technique were found to have correlation withwater injectivity index values.2. The trend found for Field-2 may not be robust when applied to another field, but it is easy to apply and seems to dowell. The correlation between the CO 2 and water injectivity index values was verified for two field cases.SPE 132624 5 ReferencesAl-Hussainy, R., Ramey, H. J. Jr., & Crawford, P. B.: “The Flow of Real Gases Through Porous Media”, Journal of Petroleum Technology, May, 1966, 624-636.Caudle, B. H., & Witte, M. D.: “Production Potential changes during Sweep-out in a Five-Spot System”, Journal of Petroleum Technology, December, 1959, 63-65.Deppe, J. C.: “Injection Rates - The Effect of Mobility Ratio, Area Swept, and Pattern”, SPE Journal, June, 1961, 81-91. Lee, J., & Wattenbarger, R. A.: Gas Reservoir Engineering, SPE Textbook Series Vol. 5, 1996.Muskat, M.: Physical Principles of Oil Production, New York: McGraw-Hill Book Company, (1949).Prats, M., Matthews, C. S., Jewett, R. L., & Baker, J. D.: “Prediction of Injection Rate and Production History for Multifluid Five-Spot Floods”, Trans. AIME, Vol. 216, 98-105, 1959.TablesWellInjectionRate,MMSCFDMeasuredBHP, psiaCalculatedBHP, psiaDifference,psia% error#1 5.8 3503 3497 -6 -0.1712 #2 4.5 3329 3381 52 1.5620 #3 4.3 3389 3380 -9 -0.2656 #4 1.6 3829 3896 67 1.750 #5 1.6 3770 3844 74 1.963 #6 4.3 3636 3659 23 0.6326 #7 3.3 3462 3479 17 0.4910 Table 1: Verification of macro with FBHP measured in injection wells6 SPE 132624 FiguresFigure 1. Plot of all Injectivity Indices for Well-1a Figure 2. Plot of all Injectivity Indices for Well-1bFigure 3. Plot of all Injectivity Indices for Well-1c Figure 4. Plot of all Injectivity Indices for Well-1dSPE 132624 7Figure 5. Well Injectivity plots for Field-1 (Mean and Standard Deviation values for the wells are given in Table 2)Figure 6. Well Injectivity plots for Field-1 (Mean and Standard Deviation values for the wells are given in Table 2)8 SPE 132624Figure 7. Well Injectivity Plots for Field-2 (Mean and Standard Deviation values for the wells are given in Table 2)Figure 8. Well Injectivity Plots for Field-2 (Mean and Standard Deviation values for the wells are given in Table 2)SPE 132624 9Figure 9. Crossplot of Water Injectivity Index and CO 2 Injectivity Index obtained from different wells in Field-2Figure 10. Water Injectivity index plot for Verification Well. Average value from this plot is used to estimate CO 2Injectivity IndexFigure 11. Graphical solution to calculate CO 2 injectionrate from injectivity indexFigure 12. Graphical solution to calculate CO 2 injectionrate from injectivity index。